Yes, that would be a good example of why this degeneracy is significant.

Another reason we care is that it greatly affects the distribution of energy among quantum levels. For example, in 3d rotation, we saw that the degeneracy of each level was 2l+1. Then, say, for l=8, we would see 17 quantum states instead of 1 (for nondegenerate levels). Basically that energy level can accommodate 16 more units of energy than a nondegenerate level.

We will soon see that this is why the p-block can accommodate 6 electrons rather than just two.

Just a quick Q of me trying to relate pchem to my gen chem knowledge. For N=2, L=0, and ml = +1,0, and -1, can ml be related to the Px, Py, and Pz orbitals? Such as Px being ml=1, the Py being ml=0, etc.

Kind of. The ml = 0 is definitely the pz. However the px is a mixture of -1 and +1 (as is the py). We will see on Monday that the three orbitals are actually po, p1 and p-1 but we'll transmogrify them to the px, py and pz.

Note that for l=0, ml can only be zero, but I think you meant to write l=1.

question 3b on the problem set has a transition from 2p-1 to 3d1. In the answer key the wavefunction PSI3,1,1 is used. Although the overall result would not change, should this wavefunction be PSI3,2,1 for 3d1?

Also, in the same problem for all three integrals it looks like a factor of sin(theta) is dropped. Is this by accident or was it consumed somewhere.